A stochastic mathematical model has been developed based upon current hypotheses of initiator-titration and iteron-handcuffing mechanisms, and tested for its ability to reproduce the experimentally derived plasmid replication rate function for the low-copy number F plasmid. The model is based on correctly-folded initiator protein monomers (folded RepE) arising from an inactive dimer pool via chaperones in limiting amounts, their random distribution to high affinity sites (iterons) at the origin (ori) and an outside locus (incC), the statistical mechanics of bound monomer participation in pairing the two loci (cis-handcuffing), and initiation probability as proportional to the number of non-handcuffed ori-saturated plasmids. Statistical factors were based on experimental iteron spacings and protein structure. RepE dimers appear to maintain nearly constant concentration with age while generating a net production of only four folded-RepE monomers per replication cycle. Provided cis-handcuffing is present, this model closely accounts for the rapid monotonic increase in the replication rate function over the host cell cycle, and reproduces the observation that replication occurs throughout the cell cycle. Present concepts of iteron-based molecular mechanisms thus appear capable of yielding a quantitative description of unit-copy-number plasmid replication dynamics. Future investigation will focus on the stability of this system as it responds to variations in plasmid number.